Sources told ESPN and MLB.com that Giants CEO Larry Baer and president of baseball operations Farhan Zaidi met with the prized free agent in Las Vegas on Tuesday. The club hasn't confirmed the meeting.
The Philadelphia Phillies are considered the front-runners to acquire Harper, although the Dodgers and Giants can provide the slugger closer proximity to his home in Las Vegas and the ability to train in Arizona for spring training, according to MLB.com.
Sources told the MLB Network that Phillies owner John Middleton also met with Harper in Vegas over the weekend, but left without a deal.
The Giants originally wanted to explore a short-term deal with Harper, but have now engaged in discussions for a 10-year deal with the slugger, according to NBC Sports Bay Area. Harper previously rejected a 10-year, $300 million deal from the Washington Nationals, who exited the bidding for their former player last week.
The 26-year-old Harper is expected to command a greater price tag than Manny Machado's $300 million, and could approach the record for guaranteed money set by Giancarlo Stanton's $325 million contract extension in 2014.
Harper had a .249 batting average with 34 home runs and a career-high 100 RBIs in 159 games with the Nationals last season. Washington selected Harper with the first-overall pick of the 2010 MLB Draft.